%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:09 PM UTC 2026
% Result : Theorem 0.19s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 8 unt; 1 def)
% Number of atoms : 187 ( 40 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 214 ( 68 ~; 61 |; 68 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 81 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( cons(X4,nil) != X2
| app(X5,cons(X4,nil)) != X3 ) ) )
| singletonP(X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( cons(X4,nil) != X2
| app(X5,cons(X4,nil)) != X3 ) ) )
| singletonP(X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f121,definition,
! [X1,X2,X3,X0] :
( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X0) )
| ~ sP0(X1,X2,X3,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f122,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X2,X3,X0)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f121]) ).
fof(f123,plain,
! [X1,X2,X3,X0] :
( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X0) )
| ~ sP0(X1,X2,X3,X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X1
& app(X5,cons(X4,nil)) = X2
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X3) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& cons(sK1(X1,X2),nil) = X1
& app(sK2(X1,X2),cons(sK1(X1,X2),nil)) = X2
& ssList(sK2(X1,X2))
& ssItem(sK1(X1,X2))
& ~ singletonP(X3) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X1,X2)),skolemize(X5,sK2(X1,X2))],[f124]) ).
fof(f126,plain,
( sK4 = sK6
& sK3 = sK5
& ( sP0(sK4,sK5,sK6,sK3)
| ( neq(sK4,nil)
& ~ neq(sK6,nil) ) )
& ssList(sK6)
& ssList(sK5)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f122]) ).
fof(f133,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f134,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK11(X0))
& cons(sK11(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0))],[f134]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ~ singletonP(X3) ),
inference(cnf_transformation,[],[f125]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X1,X2)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X1,X2),nil) = X1
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f125]) ).
fof(f146,plain,
( sP0(sK4,sK5,sK6,sK3)
| ~ neq(sK6,nil) ),
inference(cnf_transformation,[],[f126]) ).
fof(f147,plain,
( sP0(sK4,sK5,sK6,sK3)
| neq(sK4,nil) ),
inference(cnf_transformation,[],[f126]) ).
fof(f148,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f126]) ).
fof(f149,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f126]) ).
fof(f160,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f176,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f180,plain,
! [X0,X1] :
( singletonP(X0)
| ~ ssItem(X1)
| cons(X1,nil) != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f181,plain,
( sP0(sK6,sK5,sK6,sK5)
| neq(sK6,nil) ),
inference(definition_unfolding,[],[f147,f149,f148,f149]) ).
fof(f182,plain,
( sP0(sK6,sK5,sK6,sK5)
| ~ neq(sK6,nil) ),
inference(definition_unfolding,[],[f146,f149,f148]) ).
fof(f189,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f180]) ).
fof(f193,plain,
sP0(sK6,sK5,sK6,sK5),
inference(forward_subsumption_resolution,[],[f182,f181]) ).
fof(f194,plain,
~ singletonP(sK5),
inference(resolution,[],[f136,f193]) ).
fof(f225,plain,
! [X2,X3,X0,X1] :
( singletonP(X0)
| ~ ssItem(sK1(X0,X1))
| ~ ssList(X0)
| ~ sP0(X2,X0,X1,X3) ),
inference(superposition,[],[f189,f140]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( ssList(X0)
| ~ ssItem(sK1(X0,X1))
| ~ ssList(nil)
| ~ sP0(X2,X0,X1,X3) ),
inference(superposition,[],[f160,f140]) ).
fof(f229,plain,
! [X2,X3,X0,X1] :
( ssList(X0)
| ~ ssList(nil)
| ~ sP0(X2,X0,X1,X3) ),
inference(forward_subsumption_resolution,[],[f228,f137]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( singletonP(X0)
| ~ ssList(X0)
| ~ sP0(X2,X0,X1,X3) ),
inference(forward_subsumption_resolution,[],[f225,f137]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X2,X0,X1,X3)
| ssList(X0) ),
inference(forward_subsumption_resolution,[],[f229,f176]) ).
fof(f258,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X2,X0,X1,X3)
| singletonP(X0) ),
inference(forward_subsumption_resolution,[],[f232,f233]) ).
fof(f259,plain,
singletonP(sK5),
inference(resolution,[],[f258,f193]) ).
fof(f261,plain,
$false,
inference(forward_subsumption_resolution,[],[f259,f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 08:42:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/1.31 % (1029974)Detected formulas, will run a generic FOF schedule.
% 0.19/1.31 % (1029986)dis-21_1_sil=8000:lcm=predicate:random_seed=2250152537:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.19/1.31 % (1029986)Instruction limit reached!
% 0.19/1.31 % (1029986)------------------------------
% 0.19/1.31 % (1029986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1029986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1029986)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1029986)Termination reason: Instruction limit
% 0.19/1.31 % (1029986)Termination phase: Saturation
% 0.19/1.31 % (1029986)Time elapsed: 0.040 s
% 0.19/1.31 % (1029986)Peak memory usage: 90 MB
% 0.19/1.31 % (1029986)Instructions burned: 131 (million)
% 0.19/1.31 % (1029985)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2562352806:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.31 % (1029982)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3965304568:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.31 % (1029984)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=905084952:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.31 % (1029983)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3224412623:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.31 % (1029980)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=910046811:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.31 % (1029981)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=267379046:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.31 % (1029984)First to succeed.
% 0.19/1.31 % (1029984)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1029974"
% 0.19/1.31 % (1029985)Also succeeded, but the first one will report.
% 0.19/1.31 % (1029983)Instruction limit reached!
% 0.19/1.31 % (1029983)------------------------------
% 0.19/1.31 % (1029983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1029983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1029983)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1029983)Termination reason: Instruction limit
% 0.19/1.31 % (1029983)Termination phase: Saturation
% 0.19/1.31 % (1029983)Time elapsed: 0.070 s
% 0.19/1.31 % (1029983)Peak memory usage: 89 MB
% 0.19/1.31 % (1029983)Instructions burned: 109 (million)
% 0.19/1.31 % (1029988)lrs+10_1_sil=8000:sp=occurrence:random_seed=3612005367:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.19/1.31 % (1029988)Also succeeded, but the first one will report.
% 0.19/1.31 % (1029995)lrs+10_1_sil=32000:urr=on:br=off:random_seed=899699267:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.19/1.31 % (1029984)Refutation found. Thanks to Tanya!
% 0.19/1.31 % SZS status Theorem for theBenchmark
% 0.19/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (1029984)------------------------------
% 0.19/1.31 % (1029984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1029984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1029984)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1029984)Termination reason: Refutation
% 0.19/1.31 % (1029984)Time elapsed: 0.005 s
% 0.19/1.31 % (1029984)Peak memory usage: 88 MB
% 0.19/1.31 % (1029984)Instructions burned: 6 (million)
% 0.19/1.31 % (1029984)------------------------------
% 0.19/1.31 % (1029984)------------------------------
% 0.19/1.31 % (1029974)Success in time 0.45 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------